The husband of Nazanin Zaghari-Ratcliffe, the British-Iranian woman detained in Iran since April, has delivered a letter to 10 Downing Street, urging the government to do more for her release.

A day after judicial authorities in Iran announced they had formally charged the 37-year-old, her husband, Richard Ratcliffe, urged David Cameron in the letter to raise his wife’s case before leaving office on Wednesday. The two men did not meet, but Ratcliffe also intends to lobby Cameron’s successor, Theresa May, as soon as she takes the helm.

Tuesday marks 100 days since the arrest in early April of Zaghari-Ratcliffe, who is a project manager with the Thomson Reuters Foundation, the news agency’s charitable arm. She was arrested by members of the elite Revolutionary Guards at Imam Khomeini airport in Tehran, where she and her 22-month-old daughter, Gabriella, had been about to board a flight back to the UK after visiting family.

She has been behind bars since, mostly in solitary confinement – first in an unknown location near Kerman, southern Iran, and more recently in Tehran’s notorious Evin prison, where she is believed to be held in a cell with at least one other prisoner. Gabriella’s passport was confiscated and she has been placed in the care of Zaghari-Ratcliffe’s family in Iran.

“I am writing to ask you to intervene personally while it is still within your power as prime minister,” Ratcliffe wrote in his letter. “My personal view of the situation is that Nazanin and Gabriella are being held as hostages precisely because they are British. Nazanin is being held because her work for British charities and links to the outside can be used as a bogeyman in Iranian domestic politics, and because her British passport makes her a bargaining chip for international negotiations.”

He added: “100 days have already passed with them arbitrarily held in a political game. I ask you while it is still within your gift to do what you can to stop it being another 100.”

Last month, the Revolutionary Guards issued a statement accusing Zaghari-Ratcliffe of fomenting a “soft overthrow” of the Islamic Republic and being the ringleader of a network of “hostile institutions” associated with foreign intelligence agencies, allegations that her husband has called untrue and farcical.

Zaghari-Ratcliffe is the third woman with citizenship of a European country to be detained in Iran while visiting relatives. Her detention is a recent example of a string of cases involving dual nationals that has questioned Iran’s readiness in engaging with the outside world following last year’s nuclear deal.

It is still unclear why Iran is holding the Briton, but earlier this year, Iranian authorities released a group of previously detained Iranian-Americans, notably Washington Post journalist Jason Rezaian, as part of a prisoner swap with the US in exchange for a group of Iranians held in the US for crimes such as violating sanctions regulations. It is not clear if any Iranian nationals are being held in the UK for such crimes. Another British-Iranian, businessman Kamal Foroughi, 76, has also been held in Iran since May 2011.

“Three months after her arrest – which included almost seven weeks in solitary confinement – Nazanin has yet not been given access to a lawyer. She hasn’t spoken to her family in the past week,” said Monique Villa, the chief executive of Thomson Reuters Foundation.

Before her arrest, Villa said, Zaghari-Ratcliffe had been working for the charity as “a project coordinator in charge of grants applications and training, and had no dealing with Iran in her professional capacity”.

She said: “The Thomson Reuters Foundation has no dealings with Iran whatsoever, does not operate and does not plan to operate in the country. Nazanin had travelled to Iran in a personal capacity on a holiday to visit her parents as she had been doing every six months since the birth of her daughter Gabriella.”

Zaghari-Ratcliffe’s MP, Tulip Siddiq, raised her case with the foreign secretary on Tuesday at a House of Commons session. She accompanied Ratcliffe during his visit to Downing Street.

“Nazanin’s case is both upsetting and infuriating,” Siddiq told the Guardian. “A British citizen has been detained for 100 days with minimal contact with the outside world, whilst her daughter has had her passport confiscated. Yet, our government has found itself unwilling to issue any condemnation of the Iranian authorities responsible. This is completely outrageous and shows a shameful lack of commitment to British citizens’ human rights when abroad.

“As the new prime minister takes office tomorrow, she must outline her plan of action for Nazanin’s safe return. As a start, she must at least formally condemn the outrageous behaviour by a foreign government.”

Carla Ferstman, director of human rights organisation Redress, said: “Nazanin has been held for almost 100 days without access to a lawyer and without being brought before a credible judicial body. This goes against the most basic fair trial standards, whatever legal system, and it is simply unacceptable for Iran to make her and her family suffer in this way.

“Nazanin’s two-year-old daughter has been cruelly cut off from her father in the UK, as well as, of course, from being cared for by her mother. The long-term negative effects on this young family cannot be predicted.

“On Richard’s behalf we filed a petition last month with the UN working group on arbitrary detention. Iran must do the decent and proper thing and allow this mother and child to return home immediately.”